_{1}

^{*}

We initially look at a non-singular universe representation of time, and of comparing a general formula of a cosmological Potential energy as given by Padmanbhan, with Weinberg’s Quintessence Potential energy. Isolating a given time component which may serve as an introduction. We then compare this to when , and seeing what the time component then allows as far as available initial energy, the scale factor a(t) and ø , then finally admissible frequency, for Pre Planckian process generated Gravitational waves.

We follow what to expect from

as a way to quantify energy density when we have what is coming from Weinberg [

Then, look at

So, then the

And also look at Padmanabhan’s generalized inflaton potential [

We have the Hubble parameter, if before Planck time, during Plank time

Then, we could get the following variance in time,

If so, then, up to a point, in the Pre Plankian regime of space time, according to the signs on Equation (5) and Equation (6) and [

We should keep in mind that delta

Set then, in early universe conditions, let us set, if we are considering gravitons, that we will set, say that the expression below would be for pre Planckian times, with t < 10^{−}^{44} seconds. The upshot would be that there would be a GW frequency, in many cases, as a result of pre Planckian physics of greater than or equal 10^{32} Hz, which would be red shifted down to about 10^{10} Hz, i.e. a 22 order of magnitude drop, in the present era. This is assuming^{37}, as seen in [

The M as given in this would correspond to the Mass value of the universe, which is roughly 3 × 10^{55} g (where g is for grams.) [

Note that time in Equation (6) remains finite but very small, as it came out less than 10 to the minus 44 power seconds, less than Planck time, with the parameter

Equation (8) above has a minimum scale factor we can call

Furthermore, reference [

“We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett’s formulation of the ‘shortwave approximation’, which we generalize to analyze the effects of matter inhomogeneities as well as gravitational radiation. Our framework requires the metric to be close to a ‘background metric’, but allows arbitrarily large stress-energy fluctuations on small scales”.

[

Furthermore, there is another topic, to bring up, namely, the issues of the nature of determining if there is or not if there are conditions allowing for quantization in the genesis of GR, as given by [

“On the other hand, one can define Extended Theories of Gravity those semiclassical theories where the Lagrangian is modified, in respect to the standard Einstein-Hilbert gravitational Lagrangian, adding high-order terms in the curvature invariants (terms like

In Equation (9), as given, in [

“inputs into the terms

A good course starting for the experimental side to all of this, is to look at [

2.4 Stochastic searches Omni-directional gravitational wave background radiation could arise from fundamental processes in the early Universe, or from the superposition of a large number of signals with a point-like origin. Examples of the former include parametric amplification of gravitational vacuum fluctuations during the inflationary era, termination of inflation through axion decay or resonant preheating, Pre-Big Bang models inspired by string theory, and phase transitions in the early Universe.

i.e. the advantage of a correct rendering of Equation (8) we can understand if point sources are, initially an issue for relic GW, or some other initial configuration with say as given by [

[

We fit the single- and cross-frequency power spectra at frequencies ≥150 GHz to a lensed-ΛCDM model that includes dust and a possible contribution from inflationary gravitational waves (as parameterized by the tensor-to-scalar ratio r), using a prior on the frequency spectral behavior of polarized dust emission from previous/planck/analysis of other regions of the sky. We find strong evidence for dust and no statistically significant evidence for tensor modes. We probe various model variations and extensions

In the end, what we are looking for is to make sense of the following from [

An important, direct connection between the strain of relic gravitational waves and the inflaton field has been released by Dr. Corda [

Here, H is given as the evolving Hubble parameter, and

The upshot with the frequency, to this range,

End of quote from [

We seek to avoid problems of measuring dust, which wrecked the Bicep2 results, as stated in the discussion above. Note the importance of Equation (10) above, which in turn is affected by

Equation (11) may, with refinements of r = x, in the four dimensional Volume give the new HUP, in our problem, have impact upon GW generation and its relevance to Bicep 2, the search for validation of nonstandard cosmologies, and GW searches. Furthermore, as brought up in [

Note that also the value of a correct rendering of Equation (11) would be to ascertain the axial tilt as would be expected in early universe cosmology, and relic Gravitational waves, with greater precision than which showed up in the BICEP 2 results.

Refining (11), and understanding the exact particulars of input from relic frequency may allow us enough precision to avoid the Bicep 2 disaster.

This work is supported in part by National Nature Science Foundation of China grant No. 11375279.

Andrew WalcottBeckwith, (2016) Gedanken Experiment for Energy, and Scale Factor, Based upon the Assumption of Quintessence and Idea of Quantum Bounce in Order to Isolate Admissible Frequency for Gravitational Waves in the Beginning of Cosmological Evolution. Journal of High Energy Physics, Gravitation and Cosmology,02,92-97. doi: 10.4236/jhepgc.2016.21010